We assume here the reader has basic familiarity with the theory of electrical networks, and refer the reader to e.g. [1]}, [2]} for detailed background.
We recall the notations we use below.
An electrical network is a graph \(G=(V,E)\)  with edge weights or conductances \(C_e\in \mathbb {R}_+\) .
The resistance of an edge is denoted \(R_e = C_e^{-1}\) .
An unweighted graph is seen as a network with \(C_e\equiv 1\) .
We denote the resulting effective resistance between vertices \(a,b\)  by \(\operatorname{Res}(a,b)\) .
This is extended to resistance between sets \(A,B\) , denoted \(\operatorname{Res}(A,B)\) .
